I would not test -- your son is "showing" that he is gifted and unless you need a more exact number to categorize "how gifted he is" for some reason in terms of his IQ, it's not necessary right now.
I would keep the wait-and-see attitude about kindergarten. I think you're right that he may benefit quite a bit from "learning school" itself and how to play the kindergarten "game." Kindergarten is definitely much more academic in nature than it used to be when we were kids, but it's frequently still "loose" enough in style that there is quite a bit of room for enrichment if the teacher is prepared to do so. For example, while most kids in the class are doing a station on letter identification, the teacher can switch the "cards" to a WORD identification station where your son can work on words that are tricky for him when it's time for HIM to go to that station. Sometimes it's just about the logistics of letting him have "special permission" to check more than one book out of the school library a week and to get his books from whatever section he wants instead of from the "early reader" section of the school library that other kids may be limited to.
You may end up deciding that he's had enough "this is how we do school" by the end of the first semester and move him to a 1st grade classroom at that time, but you may not. It sounds like you've got a great school who is willing to work with gifted kids and allow you to advocate for him and that's 95% of the battle.